Properties

Label 2.3.ae_i
Base Field $\F_{3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $1-4x+8x^{2}-12x^{3}+9x^{4}$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.445913276015$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\zeta_{8})\)
Galois group:  $V_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2 68 626 4624 49282 532100 4898098 42614784 381715394 3486898628

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 10 24 54 200 730 2240 6494 19392 59050

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.